Integral equation methods for scattering from an impedance crack

For the scattering problem for time-harmonic waves from an impedance crack in two dimensions, we give a uniqueness and existence analysis via a combined single- and double-layer potential approach in a Hِlder space setting leading to a system of integral equations that contains a hypersingular operator. For its numerical solution we describe a fully discrete collocation method based on trigonometric interpolation and interpolatory quadrature rules including a convergence analysis and numerical examples.